introduction to linear regression analysis

Linear Regression with one Variablemodel representationAs an example of the price forecast in the above blog post, in turn, m represents the size of the training set, where the price sample number is, and x represents the input variable or feature (characteristic), where the house area is, and y is the output variable or target variable, where the house price is. (x, y) is a sample of the training set, plus

This article mainly introduces the multi-linear regression simulation curve algorithm based on PHP implementation, and analyzes the principle of the multivariate linear regression simulation curve algorithm and the relevant PHP implementation skills with the specific instance form, and the friends who need can refer to

generally divided into regression and classification. If we predict that the value is discrete, then such learning tasks are called classifications, and if the prediction is continuous, such a learning task is called regression. Unsupervised Learning: Clustering is non - supervised learning a representation algorithm that, without the given attribute characteristics, divides the given dataset into the req

is all that, don't be frightened by their namesThe above is a few basic concepts and data types introduced in Mllib, more related operations such as: summary of the matrix statistics and correlation calculation, stratified sampling, hypothesis testing, random data generation, etc. please refer to the official documentation (in fact, provide a similar static tool class, call its method can be)The following example shows the mllib of linear

(m2) $values) [1,])V2T2=e1%*%w2T2U2=f1%*%v2U2Α2=INV (t (T2)%*%t2)%*%t (T2)%*%e1 #也可由t (E1)%*%t2/norm (T2, ' 2 ') ^2 calculations α2Β2=INV (t (T2)%*%t2)%*%t (T2)%*%f1 #也可由t (F1)%*%t2/norm (T2, ' 2 ') ^2 calculations β2α2β2Library ("pls")PLS1=PLSR (y0~x0,ncomp=2,validation= ' LOO ', jackknife=t) #以下为R中pls包运算结果, showing regression results (including the squared error of the predicted value and the interpretation of the press and variance), Compared and

] = $data [$k 1][$k 2];}}/* Transpose The matrix to get the adjoint matrix */return $data 2;}/* Inverse of the matrix, the input parameter is the original matrix */Public Function Inv ($data){$m = count ($data);$n = count ($data [0]);$data 2 = [];$det _val = $this->cal_det ($data);$data 2 = $this->ajoint ($data);for ($i = 0; $i for ($j = 0; $j $data 2[$i] [$j] = $data 2[$i] [$j]/$det _val;}}return $data 2;}/* To find the product of two matrices */Public Function GetProduct ($data 1, $data 2){/*

Principle and application of Ridge regression technologyauthor Ma WenminRidge regression analysis is a biased estimation regression method dedicated to collinearity analysis, which is essentially an improved least squares estimation method, which is more consistent with the

The following is reproduced in the content, mainly to introduce the theoretical knowledge of logistic regression, first summed up the experience of their own readingIn simple terms, linear regression is a result of multiplying the eigenvalues and their corresponding probabilities directly, and the logistic regression i

Introduction to LDA algorithmA LDA Algorithm Overview:Linear discriminant Analysis (Linear discriminant, LDA), also called Fisher Linear discriminant (Fisher Linear discriminant, FLD), is a classical algorithm for pattern recognition, It was introduced in the field of patter

deviation of B, and then according to the pre-set significance level U (usually u = 0.05) and degrees of freedom (D = n-2), query the t distribution table to obtain a critical value of Tu/2, if | TB |> tu/2, it indicates that the probability of regression coefficient β = 0 is less than 0.05, And we can conclude that β = 0, that is, Y has a linear relationship with X. Otherwise, the conclusion is the opposi

Chi-Square test-investigate the correlation of categorical variables-"cross-table" or "set-table";T-Test-to investigate the correlation between continuous variables and categorical variables-"Set table";Linear logsitic Regression-study the relationship between categorical dependent variables and a set of independent variables (can be continuously classified);Tree structure Model-study the interaction betwee

unqualified sample. 4.2 LDA algorithm and PCA algorithm Based on the traditional feature face method, the researchers noticed that feature vectors (feature faces) played by feature values must be the best classification performance direction, and for K-L transformation, the differences between the images produced by external factors and the faces themselves cannot be distinguished. The feature connection reflects the differences in illumination to a large extent. Research shows that the recogni

the problem.Review the previous linear regression, a training sample given n D-dimensional features (I from 1 to n), each corresponding to a class label. We have previously made y=0 a class, and Y=1 represents another class, and now we need to make some changes to prove the relationship between least squares and LDA.is to replace 0/1 with a value.We list the least squares formulaW and is the fit weight par

. Because R2 >0.99, so this is a very obvious experimental model of linear characteristics, that is, the fitting line can be explained by more than 99.99%, covering the measured data, has a good general, can be used as a standard work curve for other unknown concentration solution measurement. To further use more metrics to describe this model, we use the "regression" tool in data

, second parameter is a non 0-dimensional subscript Collection, the third parameter is a collection of values that are non-0 Dimensions v1 = sparsevector (4,{1:3, 2:4}) # The first parameter is a dimension, the second parameter is a dictionary of subscripts and dimensions print V0.dot (v1) # calculates dot product print v0.sizeThe sparse vectors in spark can be initialized with a list or dict.Vector tags (labeled point): Vector tags are in the combination of vectors and tags, classification and

automatically output analysis recommendations, according to the suggestions we can read the meaning of the results table, self-analysis ~Further using the big data and artificial intelligence principles, Spssau system also automatically output intelligent analysis, we directly look at these words can understand the results ~ The original watering times on the nu

1. What is lda? Linear Discriminant Analysis (LDA. Fisher Linear Discriminant (linear) is a classic algorithm for pattern recognition. In 1996, belhumeur introduced Pattern Recognition and AI. The basic idea is to project a high-dimensional Pattern sample to the optimal identification vector space to extract classifica

The first satisfying condition of linear regression is the linear relationship between the dependent variable and the independent variable, and then the fitting method is based on it, but if the dependent variable and the independent variable are nonlinear, then the nonlinear regression is needed to analyze it.There ar

Linear discriminant Analysis (Linear discriminant Analyst) (i)1. QuestionsBefore we discussed the PCA, ICA or the sample data to say, can be no category tag Y. Recall that when we do the regression, if there are too many features, then there will be irrelevant features introduced, over-fitting and so on. We can use PCA

;2011Q2", "2011Q3", "2011Q4 "))The prediction result is as follows:The red triangle in the figure above is the predicted value.2. Logistic regressionLogistic regression is to predict the probability of an event by fitting the data to an online line and based on the resume curve model. You can establish a Logistic regression model using the following equations:Among them, x1, x2,...,